1

Electroweak

interactions of quarks

Benoit Clément,

Université Joseph Fourier/LPSC Grenoble

HASCO School, Göttingen, July 15-27 2012

2

PART 1 : Hadron decay,

history of flavour mixing

PART 2 : Oscillations and

CP Violation

PART 3 : Top quark and

electroweak physics

3

PART 1

Hadron decays

History of flavour mixing

4

Hadron spectroscopy

1950/1960 : lots of « hadronic states » observed

resonances in inelastic diffusion of nucleons or pions (pp,

pπ, np,…)

Multiplet structure associated with SU(2) group symmetry.

Interpreted as bound

states of strong force

Several particles

- almost same mass

- same spin

- same behavior wrt.

strong interaction

- different electric charge

5

Strange hadrons

A few particles does not fit into this scheme :

Decay time characteristic from weak interaction

Particles stable wrt. strong/EM coupling

Conserved quantum number : strangeness

Name Mass (MeV) Decay Lifetime

Λ 1116 Nπ 1.10-10s

Ξ0, Ξ-, 1320 Λπ 3.10-10s

Σ+,Σ- 1190 Nπ 8.10-11s

Σ0 1200 Λ 1.10-20s (EM)

6

Quark model

Gell-Mann (Nobel 69) and Zweig, 1963 :

hadrons are build from 3 quarks u, d and s.

Strangeness : content in strange quarks

Only weak interaction can induce change of flavour

s → Wu or s → Zd eg. 𝐵𝑅(𝐾+→𝜋+𝑣𝑣 )

𝐵𝑅(𝐾+→𝜋0𝜇+𝑣)<10-5

No Flavor Changing Neutral Currents (FCNC) in SM

7

Electroweak lagrangian

OK for

leptons

What

happens for

quarks ?

8

SU(2)L and quarks

SU(2)L symetry :

doublets of left handed fermions with ΔQ=1:

𝑢𝑑 𝐿

and sL or 𝑢𝑠 𝐿

and dL

singlets for right handed fermions : uR, dR, sR

But both Wud and Wus vertices happen !

Eg. Leptonic pion and kaon decays :

u

d

μ+

νμ

W+

+

u

s

μ+

νμ

W+

K+

9

Flavour mixing

strong interaction eigenstates (mass eigenstates)

may be different from

weak interaction eigenstates

Some mixing of d and s : 𝑑𝐶

𝑠𝐶

=U 𝑑𝑠

universality of weak interaction : conserve the

overall coupling : U +U =1

U is 2x2 rotation matrix , 1 parameter

𝑈 =cos𝜃𝐶 sin𝜃𝐶

−sin𝜃𝐶 cos𝜃𝐶 𝜽𝑪 is the Cabibbo angle (1963)

10

Back to lagrangian

1 doublet 𝑢𝑑𝐶 𝐿

and 4 singlets uR, dCR, sCR, sCL

Charged currents :

Vertices :

Wud : Wus :

𝐿𝐶𝐶 =𝑖𝑔

2 2𝜓 𝒖𝛾𝜇 1 − 𝛾5 𝜓𝒅𝑪

𝑊𝜇+ + ℎ. 𝑐.

= 𝑖𝑔𝐜𝐨𝐬𝜽𝑪

2 2𝜓 𝒖𝛾𝜇 1 − 𝛾5 𝜓𝒅𝑊𝜇

+

+𝑖𝑔𝐬𝐢𝐧𝜽𝑪

2 2𝜓 𝒖𝛾𝜇 1 − 𝛾5 𝜓𝒔𝑊𝜇

+ + ℎ. 𝑐.

−𝑖𝑔𝐜𝐨𝐬𝜽𝑪

2 2𝛾𝜇(1 − 𝛾5) −

𝑖𝑔𝐬𝐢𝐧𝜽𝑪

2 2𝛾𝜇(1 − 𝛾5)

11

Naive estimation of C

From pion and kaon lifetimes

𝜏𝜋 = 2.603 × 10−8𝑠 𝜏𝐾 = 1.23 × 10−8𝑠

u

d

μ+

νμ

W+

+

u

s

μ+

νμ

W+

K+

gcos

gsin

𝛤𝜋→𝜇𝜈 ∝ 𝑔4𝒄𝒐𝒔𝟐𝜽𝑪 𝑚𝜋

2 − 𝑚𝜇2 2

𝑚𝜋3

BR ~ 100%

𝛤𝐾→𝜇𝜈 ∝ 𝑔4𝒔𝒊𝒏𝟐𝜽𝑪 𝑚𝐾

2 − 𝑚𝜇2 2

𝑚𝐾3

BR ~ 63%

Phase

space Feynman

amplitude

𝒕𝒂𝒏𝟐𝜽𝑪 = 𝟎. 𝟔𝟑𝝉𝝅

𝝉𝑲

𝒎𝑲𝟑

𝒎𝝅𝟑

𝒎𝝅𝟐 − 𝒎𝝁

𝟐 𝟐

𝒎𝑲𝟐 − 𝒎𝝁

𝟐 𝟐⟹

𝒔𝒊𝒏𝜽𝑪= 0.265𝒄𝒐𝒔𝜽𝑪= 0.964

12

FCNC troubles

Neutral currents (d and s quark only)

𝐿𝑁𝐶 = 𝑖𝑔

2cos𝜃𝑊𝜓 𝒅𝑪

𝛾𝜇 𝑐𝑉 − 𝑐𝐴 𝛾5 𝜓𝒅𝑪𝑍𝜇 + 𝜓 𝒔𝑪

𝛾𝜇 𝑐𝑉 − 𝑐𝐴 𝛾5 𝜓𝒔𝑪𝑍𝜇

𝑐𝑉 = 𝑇 3 − 2sin2𝜃𝑊𝑄 : 𝑐𝑉 𝜓𝒅𝑪= −

1

2+

2

3sin2𝜃𝑊 𝜓𝒅𝑪

; 𝑐𝑉 𝜓𝒔𝑪=

2

3sin2𝜃𝑊 𝜓𝒔𝑪

𝑐𝐴 = 𝑇 3 : 𝑐𝐴 𝜓𝒅𝑪= −

1

2𝜓𝒅𝑪

; 𝑐𝑉 𝜓𝒔𝑪= 0

𝐿𝑁𝐶 = 𝑖𝑔

2cos𝜃𝑊𝜓 𝒅𝑪

𝛾𝜇𝑐𝑍1𝜓𝒅𝑪

𝑍𝜇 + 𝜓 𝒔𝑪𝛾𝜇𝑐𝑍

2𝜓𝒔𝑪𝑍𝜇

=𝑖𝑔

2cos𝜃𝑊𝜓 𝒅𝛾𝜇 cos2𝜃𝐶𝑐𝑍

1 + sin2𝜃𝐶𝑐𝑍2 𝜓𝒅𝑍𝜇 + 𝜓 𝒔𝛾

𝜇 sin2𝜃𝐶𝑐𝑍1 + cos2𝜃𝐶𝑐𝑍

2 𝜓𝒔𝑍𝜇

+𝑖𝑔cos𝜃𝐶sin𝜃𝐶

2cos𝜃𝑊𝜓 𝒅𝛾𝜇 𝑐𝑍

1 − 𝑐𝑍2 𝜓𝒔𝑍𝜇 + 𝜓 𝒔𝛾

𝜇 𝑐𝑍1 − 𝑐𝑍

2 𝜓𝒅𝑍𝜇

FCNC inducing term

Introducing mass eigenstates :

13

GIM and charm

Natural solution proposed by Glashow, Iliopoulos,

Maiani in 1970(GIM mechanism)

Add a 4th quark to restore the symmetry : charm

2 SU(2)L doublets + right singlets

𝑢𝑑𝐶 𝐿

,𝒄𝑠𝐶 𝐿

, uR, dCR, cR, sCR

Then the coupling to the Z becomes :

𝑐𝑍1 = 𝑐𝑍

2 = −1

2+

2

3sin2𝜃𝑊 −

1

2𝛾5

𝑖𝑔cos𝜃𝐶sin𝜃𝐶

2cos𝜃𝑊𝜓 𝒅𝛾𝜇 𝑐𝑍

1 − 𝑐𝑍2 𝜓𝒔𝑍𝜇 + 𝜓 𝒔𝛾

𝜇 𝑐𝑍1 − 𝑐𝑍

2 𝜓𝒅𝑍𝜇 =0 =0

And the FCNC terms cancel out :

14

Top and bottom

Generalization to 6 quarks : 𝑢𝑑

, 𝑐𝑠

, 𝑡𝑏

Complex 3x3 unitary matrix :

Kobayashi & Maskawa in 1973 (Nobel in 2008)

Cabibbo-Kobayashi-Maskawa or CKM Matrix

𝑉𝐶𝐾𝑀 =

𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏

𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏

𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏

, 𝑑′𝑠′𝑏′

= 𝑉𝐶𝐾𝑀

𝑑𝑠𝑏

Lepton vertex : −𝑖𝑔

2 2𝛾𝜇(1 − 𝛾5)

W+quqd vertex : −𝑖𝑔𝑽𝒒𝒖𝒒𝒅

2 2𝛾𝜇(1 − 𝛾5)

W-quqd vertex : −𝑖𝑔𝑽𝒒𝒖𝒒𝒅

∗

2 2𝛾𝜇(1 − 𝛾5)

15

CKM matrix

𝑉𝐶𝐾𝑀 =

𝑉𝑢𝑑 𝑉𝑢𝑠 𝑉𝑢𝑏

𝑉𝑐𝑑 𝑉𝑐𝑠 𝑉𝑐𝑏

𝑉𝑡𝑑 𝑉𝑡𝑠 𝑉𝑡𝑏

=

0.97428 ± 0.00015 0.2253 ± 0.0007 0.00347−0.00012+0.00016

0.2252 ± 0.0007 0.97345−0.00016+0.00015 0.0410−0.0007

+0.0011

0.00862−0.00020+0.00026 0.0403−0.0007

+0.0011 0.999152−0.000045+0.000030

First approximation : Diagonal matrix 𝑉𝐶𝐾𝑀 =1 0 00 1 00 0 1

no family change : Wud, Wcs and Wtb vertices

Second approximation : Block matrix 𝑉𝐶𝐾𝑀 =𝑉𝑢𝑑 𝑉𝑢𝑠 0𝑉𝑐𝑑 𝑉𝑐𝑠 00 0 1

submatrix is almost the Cabibbo matrix

Vud ≈ Vcs ≈ cosC and Vus ≈ Vcd ≈ sinC

Top quark only decays to bottom quark

Charm quark mostly decays to strange quark

Bottom and Strange decays are CKM suppressed

16

PART 2

Oscillations and

CP Violation

17

Discrete symmetries

3 discrete symmetries, such as 𝐒 ²=1

Affects : coordinates, operators, particles fields

𝐏 = Parity : space coordinates reversal : 𝒙 → −𝒙

𝐂 = Charge conjugaison : particle to antiparticle

transformation (i.e. inversion of all conserved

charges, lepton and baryon numbers)

eg. 𝒆−𝑪

𝒆+, 𝒖𝑪

𝒖 , 𝝅−(𝒅𝒖 )𝑪

𝝅+(𝒖𝒅 ),𝑲𝟎(𝒅𝒔 )𝑪

𝑲𝟎(𝒔𝒅 )

𝐓 = Time : time coordinate reversal : 𝒕 → −𝒕

18

Parity

Weak interaction is not invariant

under parity :

maximum violation of parity

(C.S.Wu experiment on 60Co beta

decay)

Strong and EM interaction are OK.

Parity does not change the nature of particles parity

eigenstates : 𝐏 𝒑 = 𝒑

: Intrinsic partity since 𝐏 ²=1, =1

Under 𝑷 : 𝑬 → −𝑬, vector; 𝑩 → 𝑩, pseudovector

4 -potential : 𝝓, 𝑨 → 𝝓, −𝑨 so : 𝜂𝑝ℎ𝑜𝑡𝑜𝑛 = −1

Strong and EM interaction conserves parity.

19

2 photons, helicity=+1 2 photons, helicity= -1

Parity of the pion

EM decay : 0→, conserves parity

Parity eigenstates for photon pair :

Pions can only decay in one of these states

0

e-

e+

e+

e-

J=0 𝟐

𝟏

+ = 1 + 2

2, 𝜂 = 1

− = 1 − 2

2, 𝜂 = −1

Measure angular distribution

of e+e- pairs :

+ ∶ 1 + cos2φ − ∶ 1 − cos2φ

Experimentally : 𝜼𝝅𝟎 = −𝟏

20

CP symmetry : pion decay

π+ scalar

νμ left-handed

μ+

J=0, J3= 0

J=1/2

J3=-1/2

J=1/2

J3=+1/2 k

-k

π+ scalar

μ+

νμ left-handed, massless

chirality = helicity

J=0, J3= 0

J=1/2

J3=+1/2

J=1/2

J3=-1/2 k

-k

π- scalar

μ-

νμ right-handed

J=0,J3= 0

J=1/2

J3=+1/2

J=1/2

J3=-1/2 k

-k

C

C

P P

CP

π- scalar

νμ right-handed

J=0, J3= 0

J=1/2

J3=-1/2

J=1/2

J3=+1/2 k

-k μ-

21

CP symmetry : neutral kaons

Kaons are similar to pions :

→ same SU(3) octet pseudoscalar mesons

𝑷 𝑲𝑶 = − 𝑲𝑶

and 𝑷 𝑲𝑶 = − 𝑲𝑶

K0 (=us) and K0 (=us) are antiparticle of each other

𝑪 𝑲𝑶 = 𝑲𝑶 and 𝑪 𝑲𝑶 = 𝑲𝑶

So: 𝐶 𝑃 𝐾𝑂 = − 𝐾𝑂 and 𝐶 𝑃 𝐾𝑂 = − 𝐾𝑂

Then CP-eigenstates are :

Does weak currents conserve CP ?

𝐾10 =

𝐾0 − 𝐾0

2, 𝜂𝐶𝑃 = 1 𝐾2

0 = 𝐾0 + 𝐾0

2, 𝜂𝐶𝑃 = −1

22

CP violation in Kaon decays

If CP is conserved by weak interactions then only

𝐾10 ⟶ 𝜋𝜋, (𝜂𝐶𝑃 = 1) and 𝐾2

0 ⟶ 𝜋𝜋𝜋, 𝜂𝐶𝑃 = −1

With a longer lifetime for 𝐾20 (more vertices)

Experimentally : 1=0.9x10-10s 2=5.2x10-8s

After t>>1 only the long-lived components remains

but a few 2 pions decays are still observed !

Cronin & Fitch, 1964, Nobel 1980

Conclusion : the long lived component isn’t a pure

CP eigenstate : small CP violation !

Physical states : 𝐾𝐿0 =

𝐾10 − 𝐾2

0

1+ 2, 𝐾𝑆

0 = 𝐾1

0 + 𝐾20

1+ 2

𝜀 = 2.3 × 10−3

23

Meson oscillations

Neutral pseudoscalar mesons 𝑃 and 𝑃 (K0, D0, B0, BS)

Propagation/strong interaction Hamiltonian : 𝐻 0

𝐻 0 𝑃 = 𝑚𝑃 𝑃 , 𝐻 0 𝑃 = 𝑚𝑃 𝑃 (in rest frame)

Interaction (weak) states ≠ propagation states.

Decay is allowed : effective hamiltonian 𝐻 𝑊 is not hermitian

𝐻 𝑊 = 𝑀 − 𝑖𝛤

2 with 𝑀 =

𝐻 𝑊+𝐻 𝑤†

2 𝛤 = 𝐻 𝑊 − 𝐻 𝑤

† hermitian

For eigen states : 𝑀 =𝑚1 00 𝑚2

𝛤 =𝛾1 00 𝛾2

And the time evolution of state 1 is :

𝑃1(𝑡) = 𝑒−𝑖𝑚1𝑡𝑒−𝛾1𝑡

2 𝑃1(0) 𝐼 𝑡 = 𝑃1 0 𝑃1 𝑡 2 = 𝑒−𝛾1𝑡

Exponential decay : 𝑀 mass matrix, 𝛤 decay width

24

Interaction eigenstates

In the basis 𝑃 , 𝑃 , the 2 states have the same properties

(CPT symmetry) : 𝑀11 = 𝑀22 ≡ 𝑀0 and 𝛤11 = 𝛤22 ≡ 𝛤0

If we assume 𝑀 , 𝛤 to be real : 𝑀12 = 𝑀21 ≡ 𝑀 and 𝛤12 = 𝛤21 ≡ 𝛤

Then : 𝐻 𝑊 =𝑀0 − 𝑖

𝛤0

2𝑀 − 𝑖

𝛤

2

𝑀 − 𝑖𝛤

2𝑀0 − 𝑖

𝛤0

2

In new basis :

𝑃𝐿 : long lived, mass 𝑀𝐿 = 𝑀0 + 𝑀 and width 𝛤𝐿 = 𝛤0 + 𝛤 ≪ 𝛤0

𝑃𝑆 : short lived, mass 𝑀𝑆 = 𝑀0 − 𝑀 and width 𝛤𝑆 = 𝛤0 − 𝛤 ≈ 𝛤0

𝑷𝑳 = 𝑷 + 𝑷

𝟐

𝑷𝑺 = 𝑷 − 𝑷

𝟐

𝑯 𝑾 =𝑴𝟎 + 𝑴 − 𝒊

𝜞𝟎 + 𝜞

𝟐𝟎

𝟎 𝑴𝟎 − 𝑴 − 𝒊𝜞𝟎 − 𝜞

𝟐

From perturbation theory : 𝜞 ≈ −𝜞𝟎

25

Time evolution

General state : mixing of 𝑃𝐿 and 𝑃𝑆 :

Coefficients cL and cS satisfy the Schrödinger eq. :

Then time evolution is :

𝑃 (𝑡) = 𝑐𝐿 𝑡 𝑃𝐿 + 𝑐𝑆 𝑡 𝑃𝑆

𝑖𝑑

𝑑𝑡

𝑐𝐿 𝑡

𝑐𝑆 𝑡=

𝑀𝐿 − 𝑖1

2Γ𝐿 0

0 𝑀𝑆 − 𝑖1

2Γ𝑆

𝑐𝐿 𝑡

𝑐𝑆 𝑡

𝑃 (𝑡) = 𝑒−𝑖𝑀0𝑡 𝑐𝐿 0 𝑒𝑖𝑀 𝑡−Γ𝐿𝑡2 𝑃𝐿 + 𝑐𝑆 0 𝑒−𝑖𝑀 𝑡−

Γ𝑆𝑡2 𝑃𝑆

26

Time evolution

For the Kaon system :

m = 3.48x10-12 MeV = 5.29 ns-1

S= 89.6 ps

L= 51.2 ns

For a pure 𝑷 initial state : 𝒄𝑳 𝟎 = 𝒄𝑺 𝟎 =𝟏

𝟐.

And the intensity after a given time is :

𝐼 𝑡 = 𝑃 𝑃 𝑡 2 =

1

4𝑒−Γ𝐿𝑡 + 𝑒−Γ𝑆𝑡 + 𝟐𝒆−

𝜞𝑳+𝜞𝑺𝟐 𝒕𝐜𝐨𝐬 (𝟐𝑴 𝒕)

Oscillations 𝑃𝐿 𝑃𝑆 in time,

with a frequency equal to the

mass difference :

𝜟𝒎 = 𝑴𝑳 − 𝑴𝑺 = 𝟐𝑴

27

CP violation

Previously we assumed 𝑀 and 𝛤 to be real

Interaction eigenstates = CP-eigenstates

But if complex 𝑀12 = 𝑀21∗ and 𝛤12 = 𝛤21

∗

Then the eigenstates ares :

Complex mass matrix induces CP-violation

𝑃𝐿 = 𝑁 𝑃 + 𝜀 𝑃 𝑃𝑆 = 𝑁 𝑃 − 𝜀 𝑃

𝜀 =𝑀12

∗ −𝑖2 𝛤12

∗

𝑀12 −𝑖2 𝛤12

𝑁−2 = 1 +𝑀12

2+

1

4Γ12

2+𝐼𝑚(𝛤12

∗ 𝑀12)

𝑀122+

1

4Γ12

2−𝐼𝑚(𝛤12

∗ 𝑀12)

28

Parametrization of CKM

3x3 complex unitary matrix has 4 parameters

3 angles :

𝛼 = 𝜑13 = 𝑎𝑟𝑔 −𝑉𝑡𝑑𝑉𝑡𝑏

∗

𝑉𝑢𝑑𝑉𝑢𝑏∗ , 𝛽 = 𝜑23 = 𝑎𝑟𝑔 −

𝑉𝑐𝑑𝑉𝑐𝑏∗

𝑉𝑡𝑑𝑉𝑡𝑏∗ , 𝛾 = 𝜑12 = 𝑎𝑟𝑔 −

𝑉𝑢𝑑𝑉𝑢𝑏∗

𝑉𝑐𝑑𝑉𝑐𝑏∗

1 complex phase :

Complex phase

allows CP violation

𝑉𝐶𝐾𝑀 =

𝑐12𝑐13 𝑠12𝑐13 𝑠13𝑒𝑖𝛿

−𝑠12𝑐23 − 𝑐12𝑠23𝑠13𝑒−𝑖𝛿 𝑐12𝑐23 − 𝑠12𝑠23𝑠13𝑒−𝑖𝛿 𝑠23𝑐13

𝑠12𝑠23 − 𝑐12𝑐23𝑠13𝑒−𝑖𝛿 −𝑐12𝑠23 − 𝑠12𝑐23𝑠13𝑒−𝑖𝛿 𝑐23𝑐13

u

d

μ+

νμ

W+

+

Vcs

V*cd

Vus

29

Oscillation and boxes

Quark interpretation : box diagram

The mass matrix off-diagonal elements becomes:

𝑀12 = 𝐶 𝑉𝑢𝑠∗ 𝑉𝑢𝑑𝑚𝑢 + 𝑉𝑐𝑠

∗ 𝑉𝑐𝑑𝑚𝑐 + 𝑉𝑡𝑠∗ 𝑉𝑡𝑑𝑚𝑡

2

= 𝐶 𝑉𝑢𝑠∗ 𝑉𝑢𝑑(𝑚𝑢−𝑚𝑐) + 𝑉𝑡𝑠

∗ 𝑉𝑡𝑑(𝑚𝑡 − 𝑚𝑐) 2

Complex because of phase in CKM matrix :

CP violation :

can only happen if at least 3 families.

only happens in loop diagrams : rare decays

and oscillations.

30

Unitarity triangles

𝑉𝑢𝑑𝑉𝑢𝑠∗ + 𝑉𝑐𝑑𝑉𝑐𝑠

∗ + 𝑉𝑡𝑑𝑉𝑡𝑠∗ = 0

𝑽𝒖𝒅𝑽𝒖𝒃∗ + 𝑽𝒄𝒅𝑽𝒄𝒃

∗ + 𝑽𝒕𝒅𝑽𝒕𝒃∗ = 𝟎

𝑉𝑢𝑠𝑉𝑢𝑑∗ + 𝑉𝑐𝑠𝑉𝑐𝑑

∗ + 𝑉𝑡𝑠𝑉𝑡𝑑∗ = 0

𝑉𝑢𝑠𝑉𝑢𝑏∗ + 𝑉𝑐𝑠𝑉𝑐𝑏

∗ + 𝑉𝑡𝑠𝑉𝑡𝑏∗ = 0

𝑉𝑢𝑏𝑉𝑢𝑑∗ + 𝑉𝑐𝑏𝑉𝑐𝑑

∗ + 𝑉𝑡𝑏𝑉𝑡𝑑∗ = 0

𝑉𝑢𝑏𝑉𝑢𝑠∗ + 𝑉𝑐𝑏𝑉𝑐𝑠

∗ + 𝑉𝑡𝑏𝑉𝑡𝑠∗ = 0

Unitarity of CKM matrix :

𝑉𝐶𝐾𝑀† 𝑉𝐶𝐾𝑀=1

𝑉𝑢𝑑𝑉𝑢𝑑

∗ + 𝑉𝑢𝑠𝑉𝑢𝑠∗ + 𝑉𝑢𝑏𝑉𝑢𝑏

∗ = 1 𝑉𝑐𝑑𝑉𝑐𝑑

∗ + 𝑉𝑐𝑠𝑉𝑐𝑠∗ + 𝑉𝑐𝑏𝑉𝑐𝑏

∗ = 1 𝑉𝑡𝑑𝑉𝑡𝑏

∗ + 𝑉𝑡𝑠𝑉𝑡𝑠∗ + 𝑉𝑡𝑏𝑉𝑡𝑏

∗ = 1

Sum of 3 complex numbers :

triangle in complex plane

Complex only if CP violating

phase is large

Most triangle are almost flat,

except one.

31

Unitarity triangles

Many decay processes, including rare decays of

strange/charmed/beauty hadrons

- Some sensitive to matrix elements Vxy

- Some sensitive mass differences (oscillations)

- Some sensitive to angles (CP-violation)

32

Experiments

PAST :

e+e-, at (4S) resonnance

(bb state)

BELLE (KEK, Japan)

BaBAR (SLAC, US)

pp : CDF and D0

PRESENT pp : LHCb

(+ ATLAS/CMS)

FUTURE : e+e- SuperBELLE (Japan) SuperB (Italy)

33

PART 3

Top quark and

electroweak physics

34

Top quark decays

Top quark only decays through weak interaction

Vtb ~1 : t→Wb at 100%

mt > mW+mb : only quark that decays with a real W

Coupling not « weak » : top ~10-25s >> hadronization

No loss of polarization.

Top quark signature :

1 central b-quark jet, with

high pT (~70 GeV)

1 on-shell W boson :

1 isolated lepton

and ET (~35 GeV)

or 2 jets (~35 GeV)

35

Top quark production

σNLO ≈ 3 pb

σNLO ≈ 65 pb

σNLO ≈ 15 pb

σNLO ≈ 160 pb

Strong interaction

top/antitop pairs Weak interaction

tb, tq(b)

Weak interaction

tW

√s=7TeV

36

Top quark and electroweak

Top quark decays through Wtb vertex - Use pair production (largest cross-section)

- Probe V-A theory in top coupling

- Measure Vtb assuming 3 generations

Electroweak production of the top quark - lower cross-section, more background

- cross-section gives access to Vtb without

assumptions on unitarity

- sensitivity to new physics (W’, 4th generation…)

Precision measurement of mass and coupling - all electroweak quantities are linked at higher order

- Sensitivity to the Higgs sector (high mass)

37

W helicity in top decays (1)

Longitudinal W

F0 ≈ 0.7

t b

W

+1/2

-1/2

+1

t W

b

+1/2 +1

-1/2

t W

b

+1/2

+1/2

0

Left-handed W

FL ≈ 0.3

Right-handed W

FR ≈ 0

Like for muon decays : mb << mt, mW

chirality = helicity

right-handed W is strongly suppressed

38

W helicity in top decays (2)

In theory :

Nice and easy

In practice :

Expected

shapes for

ATLAS

experiment

Angle between top and lepton

in W rest frame

Also possible : unfolding…

39

ATLAS results 1fb-1

The Model stays

boringly Standard

40

Top decays and Vtb

CL 95% @ 64.0

03.1 19.0

17.0

R

R

2tb2

tb2

td2

ts

2tb |V|

|V||V||V|

|V|

Wq)B(t

Wb)B(tR

Very old D0

result

Lepton+jets

(~230 pb-1)

B-jets can be identified : long lifetime of b-hadrons,

larger mass, fragmentation…

εbtag~60%, mistag~0.1%

Use events with 0 b-tag, 1 b-tag and 2 b-tag

Simutaneous measurment of σtt and R

Likelihood discriminant

41

Single top

Only t-channel has been clearly (>5σ)

seen at Tevatron and LHC.

First 3σ evidence for tW (ATLAS)

42

Direct Vtb

measurement

All 3 diagrams feature

1Wtb vertex

σ|Vtb|²

43

Standard Model consistancy

Top mass is one of the ingredients of the electroweak fit

indirect contraints on the Higgs mass

Radiative corrections (1 loop)

to the W mass